recursive adaptive filter

recursive adaptive filter - 1 Computer exercise 5:...

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1 Computer exercise 5: Recursive Least Squares (RLS) This computer exercise deals with the RLS algorithm. The example applica- tion is adaptive channel equalization, which has been introduced in compu- ter exercise 2. A description can be found in Haykin, edition 4, chapter 5.7, pp. 285-291, (edition 3: chapter 9.7, pp. 412-421), Computer Experiment on Adaptive Equalization (using the LMS algorithm). In this exercise you should compare the RLS algorithm and the LMS algorithm. An implementation of the LMS algorithm can be downloaded form the course web page, computer exercise 2. Computer exercise 5.1 The RLS update equations are given by k ( n ) = λ - 1 P ( n - 1) u ( n ) 1 + λ - 1 u H ( n ) P ( n - 1) u ( n ) ξ ( n ) = d ( n ) - h w ( n - 1) u ( n ) h w ( n ) = h w ( n - 1) + k ( n ) ξ * ( n ) P ( n ) = λ - 1 P ( n - 1) - λ - 1 k ( n ) u H ( n ) P ( n - 1) . Create a function in Matlab that takes an input vector u and a reference signal d , both of length N , and calculates the error xi for all time instants. function [xi,w]=rls(lambda,M,u,d,delta) % Recursive Least Squares % Call: % [xi,w]=rls(lambda,M,u,d,delta); % % Input arguments: % lambda = forgetting factor, dim 1x1 % M = filter length, dim 1x1 % u = input signal, dim Nx1 % d = desired signal, dim Nx1 % delta = initial value, P(0)=delta^-1*I, dim 1x1 % % Output arguments: % xi = a priori estimation error, dim Nx1 % w = final filter coefficients, dim Mx1 Use h w (0) = [0 , 0 ,..., 0] T as initial values for the Flter coe±cients. ²or the initial value of the inverse matrix P (0) choose a diagonal matrix with the Adaptive Signal Processing 2007 Computer exercise 5
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2 value δ - 1 on the main diagonal. In Matlab this is done by P=eye(M)/delta; , where eye returns an identity matrix of size M . Mind the correct order of u ( n ) = [ u ( n ) ,u ( n - 1) ,...,u ( n - M + 1)] T ! In Matlab this is best done by
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This note was uploaded on 04/14/2010 for the course EE EE 500 taught by Professor Alijadbabaie during the Fall '03 term at Penn College.

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recursive adaptive filter - 1 Computer exercise 5:...

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